Question

show that the equation has a root in the given interval 3x^3-2x^2+5x+4=0 [-1,0]

Answer 1

so use the intermediate value theorem. at -1, the function = -6. at 0, the function = 4. since the function is continuous, it must pass the x-axis in the interval -1 to 0. at that point, you have the root.

hope this is helpful

Answer 2

3(-1)^3 - 2(-1)^2 + 5(-1) + 4
3(-1) - 2(1) - 5 + 4
-3 -2 -5 + 4
-6

3(0)^3 - 2(0)^2 + 5(0) + 4
3(0) -2(0) + 0 + 4
0 + 0 + 0 + 4
4

because at x = -1 , y = -6
and at x = 0, y = 4

the graph had to cross the x axis so there must be a root there.